CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 7 - MCQExams.com

If $$\cos ^{ -1 }{ \left( \cfrac { p }{ a }  \right)  } +\cos ^{ -1 }{ \left( \cfrac { p }{ b }  \right)  } =\alpha $$, then $$\cfrac { { p }^{ 2 } }{ { a }^{ 2 } } +k\cos { \alpha  } +\cfrac { { p }^{ 2 } }{ { b }^{ 2 } } =\sin ^{ 2 }{ \alpha  } $$, where $$k$$ is equal to
  • $$\cfrac { 2pq }{ ab } $$
  • $$-\cfrac { 2pq }{ ab } $$
  • $$-\cfrac { pq }{ ab} $$
  • $$\cfrac { pq }{ ab } $$
The number of solutions of the equation $$\sin\theta +\cos\theta =\sin 2\theta$$ in the interval $$[-\pi, \pi]$$ is?
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
The number of real solutions of the equation $$2\sin 3x+\sin 7x-3=0$$ which lie in the interval $$[-2\pi, 2\pi]$$ is?
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
If $$\sin x =$$ $$\cos^2x$$, then $$\cos^2x (1 + \cos^2x)$$ is equal to 
  • $$0$$
  • $$1$$
  • $$2$$
  • None of these
Find the value of $$\tan { 1 } \tan { 2 } ....\tan { 89 } $$
  • $$-1$$
  • $$1$$
  • $$\sqrt 2$$
  • $$2$$
The value of $$\cos ^{ 4 }{ \left( \cfrac { \pi  }{ 8 }  \right)  } +\cos ^{ 4 }{ \left( \cfrac { 3\pi  }{ 8 }  \right)  } +\cos ^{ 4 }{ \left( \cfrac { 5\pi  }{ 8 }  \right)  } +\cos ^{ 4 }{ \left( \cfrac { 7\pi  }{ 8 }  \right)  } $$ is
  • $$0$$
  • $$1/2$$
  • $$3/2$$
  • $$1$$
Let $$X = \left \{x\epsilon \mathbb {R} : \cos (\sin x) = \sin (\cos x)\right \}$$. The number of solutions of $$X$$ is?
  • $$0$$
  • $$2$$
  • $$4$$
  • Not finite
The principal solution of $$\sec x = \dfrac {2}{\sqrt {3}}$$ are
  • $$\dfrac {\pi}{3}, \dfrac {11\pi}{6}$$
  • $$\dfrac {\pi}{6}, \dfrac {11\pi}{6}$$
  • $$\dfrac {\pi}{4}, \dfrac {11\pi}{4}$$
  • $$\dfrac {\pi}{3}, \dfrac {11\pi}{4}$$
The equation $$2\tan { x } +5x-2=0$$ has:
  • no solution in $$\left[ 0,\dfrac{\pi}{4} \right] $$
  • at least one real solution in $$\left[ 0,\dfrac{\pi}{4} \right] $$
  • two real solution in $$\left[ 0,\dfrac{\pi}{4} \right] $$
  • None of these
The expression $${ \left( \tan { \theta  } +\sec { \theta  }  \right)  }^{ 2 } $$is equal to
  • $$\cfrac { 1+\cos { \theta } }{ 1-\cos { \theta } } $$
  • $$\cfrac { 1+\sin { \theta } }{ 1-\sin { \theta } } $$
  • $$\cfrac { 1-\cos { \theta } }{ 1+\cos { \theta } } $$
  • $$\cfrac { 1-\sin {\theta } }{ 1+\sin { \theta } } $$
$$\dfrac {\tan \theta}{1 +\tan^{2} \theta} + \dfrac {\cot \theta}{(1 + \cot^{2}\theta)^{2}}$$ is equal to
  • $$2\sin \theta \cdot \cos \theta$$
  • $$\text{cosec} \theta \cdot \sec \theta$$
  • $$\sin \theta \cdot \cos \theta$$
  • $$2\text{cosec} \theta \cdot \sec \theta$$
If $$\sin \alpha + \cos \alpha = k$$, then $$|\sin \alpha - \cos \alpha |$$ equals.
  • $$\sqrt {2 - k^{2}}$$
  • $$\sqrt {k^{2} - 2}$$
  • $$|k|$$
  • $$\sqrt {2} - k$$
  • $$k - \sqrt {2}$$
If $$n = \dfrac {\cos \alpha}{\cos \beta}, m = \dfrac {\sin \alpha}{\sin \beta}$$, then $$(m^{2} - n^{2})\sin^{2}\beta$$ is
  • $$1 - n$$
  • $$1 + n$$
  • $$1 - n^{2}$$
  • $$1 + n^{2}$$
If $$\sin { \theta } =\cfrac { 8 }{ 17 } $$ where $${ 0 }^{ o }<\theta <{ 90 }^{ o }$$, then $$\tan { \theta  } +\sec { \theta  } $$ is
  • $$\dfrac {1}{3}$$
  • $$\dfrac {2}{3}$$
  • $$\dfrac {4}{3}$$
  • $$\dfrac {5}{3}$$
$$\cfrac { 3-4\sin ^{ 2 }{ \theta  }  }{ \cos ^{ 2 }{ \theta  }  } $$ is equal to
  • $$3-\cot ^{ 2 }{ \theta } $$
  • $$3+\cot ^{ 2 }{ \theta } $$
  • $$3-\tan ^{ 2 }{ \theta } $$
  • $$3+\tan ^{ 2 }{ \theta } $$
$$\sec^26 + \text{cosec}^26 $$ is equal to:
  • $$\sec^26. \cot^26$$
  • $$\sec^26 .\tan^26$$
  • $$\text{cosec}^26. \cot^26$$
  • $$\text{cosec}^26. \sec^26$$
$$\sin { \theta  } +\cos { \theta  } =\sqrt { 2 } $$ and $$\theta$$ is acute, then $$\tan{\theta}$$ is
  • $$\dfrac {1}{\sqrt { 3 } }$$
  • $$1$$
  • $$\sqrt { 3 } $$
  • $$\infty$$
If $$\tan { \theta  } =\dfrac {3}{4} $$ and $$0<\theta <{ 90 }^{ 0 }$$, then the value of $$\sin { \theta  } \cos { \theta  } $$ is
  • $$\dfrac {1}{5}$$
  • $$\dfrac {9}{5}$$
  • $$\dfrac {12}{25}$$
  • $$\dfrac {25}{12}$$
$$\left( \text{cosec} { \theta  } -\sin { \theta  }  \right) \left( \sec { \theta  } -\cos { \theta  }  \right) \left( \tan { \theta  } +\cot { \theta  }  \right) $$ simplifies to
  • $$0$$
  • $$1$$
  • $$\tan { \theta } $$
  • $$\cot { \theta } $$
The expression $$3(\sin x - \cos x)^{4} + 6(\sin x + \cos x)^{2} + 4(\sin^{6}x + \cos^{6}c)$$ is equal to
  • $$10$$
  • $$11$$
  • $$12$$
  • $$13$$
$$(\sin \theta + \cos \theta)(1 - \sin \theta \cos \theta)$$ can be written as
  • $$\sin \theta + \cos \theta$$
  • $$\sin^{3} \theta - \cos^{3}\theta$$
  • $$\sin^{3}\theta + \cos^{3}\theta$$
  • $$\sin \theta - \cos \theta$$
$$\sin ^{ 6 }{ \theta  } +\sin ^{ 2 }{ \theta  } \cos ^{ 2 }{ \theta  } -\sin ^{ 4 }{ \theta  } \cos ^{ 4 }{ \theta  } -\cos ^{ 6 }{ \theta  } $$ equals to
  • $$\sin ^{ 2 }{ \theta } -\cos ^{ 3 }{ \theta } $$
  • $$\sin ^{ 3 }{ \theta } -\cos ^{ 3 }{ \theta } \quad $$
  • $$\sin ^{ 4 }{ \theta } +\cos ^{ 4 }{ \theta } $$
  • $$\sin ^{ 2 }{ \theta } -\cos ^{ 2 }{ \theta } $$
$$\left( 1-\sin ^{ 2 }{ \theta  }  \right) \left( 1+\tan ^{ 2 }{ \theta  }  \right) $$ is equal to
  • $$1$$
  • $$1.5$$
  • $$2$$
  • $$2.5$$
$$\tan { \theta  } \left( 1-\cot ^{ 2 }{ \theta  }  \right) $$ is equal to
  • $$\cot { \theta } \left( 1-\tan ^{ 2 }{ \theta } \right) $$
  • $$\cot { \theta } \left( \tan ^{ 2 }{ \theta } -1 \right) $$
  • $$\cot { \theta } \tan ^{ 2 }{ \theta } $$
  • $$\tan { \theta } co\sec ^{ 2 }{ \theta } $$
If $$2\cos A+3\cos  B+5\cos C$$$$=2\sin A+3\sin B+5\sin C=0$$ then
$$8\cos 3A+27\cos 3B+125\cos C$$$$=k\cos(A+B+C)$$  then $$k=$$
  • $$70$$
  • $$80$$
  • $$90$$
  • $$60$$
If $$\sin \left(\sin^{-1}\dfrac{1}{5}+\cos ^{-1}x\right)=1$$, then find the value of $$x$$.
  • $$-\dfrac{1}{5}$$
  • $$\dfrac{1}{2}$$
  • $$-\dfrac{1}{2}$$
  • $$\dfrac{1}{5}$$
Solve:
$$\dfrac{\cot \theta+\text{cosec }\theta-1}{\cot\theta-\text{cosec }\theta+1}$$
  • $$\dfrac{1+\cos \theta}{\sin\theta}$$
  • $$\dfrac{\sin\theta}{1-\cos\theta}$$
  • $$\dfrac{1-\cos\theta}{\sin\theta}$$
  • $$\dfrac{\cos\theta}{1-\sin\theta}$$
If $$\cos { \theta  } -\sin { \theta  } =\sqrt { 2 } \sin { \theta  } $$, then $$\cos { \theta  } +\sin { \theta  } $$ is
  • $$\sqrt { 2 } \cos { \theta } $$
  • $$\sqrt { 2 } \sin { \theta } $$
  • $$0$$
  • $$1$$
If $$\theta$$ and $$\phi $$ are angles in the first quadrant such that $$\tan { \theta  } =\dfrac 17$$ and $$\sin { \phi  } =\dfrac {1}{\sqrt { 10 }} $$, then 
  • $$\theta +2\phi ={{90 }}^{o} $$
  • $$\theta +2\phi ={{ 30 }}^{o} $$
  • $$\theta +2\phi ={{ 75 }}^{o} $$
  • $$\theta +2\phi ={{45}}^{o} $$
The value of 
$$\cos { \left( \pi /5 \right)  } \cos { \left( 2\pi /5 \right)  } \cos { \left( 4\pi /5 \right)  } \cos { \left( 8\pi /5 \right)  } $$ is 
  • $$\dfrac{1}{16}$$
  • $$0$$
  • $$\dfrac{-1}{8}$$
  • $$\dfrac{-1}{16}$$
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